Fundamental limits of radio interferometers:
Source parameter estimation
Cathryn Trott
Randall Wayth
Steven Tingay
Curtin University
International Centre for Radio Astronomy Research (ICRAR)
How do the limits of the instrument and
our methods impact our measurements?
Deconvolution artifacts
Dataset information
content
Fundamental limits of
radio
Interferometers:
- dynamic range
- parameter estimation
Calibration
Ionosphere
Pointing errors
Primary beam errors
Image space noise
correlations
(Fourier transform)
How do the limits of the instrument and
our methods impact our measurements?
Deconvolution artifacts
Dataset information
content
Focus on
estimation
limits of dataset
Fundamental limits of
radio
Interferometers:
- dynamic range
- parameter estimation
Calibration
Ionosphere
Pointing errors
Primary beam errors
Image space noise
correlations
(Fourier transform)
Science drives configuration:
what is the impact of array layout?
MWA configuration (Beardsley et al. 2012)
Hypothetical 128 antenna configuration
- EoR/diffuse emission - short
Same longest baseline and
number of antennas
Science
- Fine structures - long
- Source localization - long
How do changing observing conditions
affect our ability to calibrate?
Wide-field observations: sources in
sidelobes, distortion at field edges


Non-stationary point spread functions
Low-frequency observations –
ionospheric refraction of wavefront:
 Beam changes on short
timescales (secs-mins)

Cohen & Rottgering (2009)
Instrument calibration on short timescales
→ observe bright sources, fit positions, remove from dataset (e.g., peeling)
→ impact??
Measurement conditions changing:
require short timescale calibration
Current paradigm
New paradigm

Small number of elements

Large number of elements

Moderate primary beam

Wide field-of-view
Stable
atmosphere/ionosphere
(high frequency)

Varying
atmosphere/ionosphere
(low frequency)


Long integrations

Snapshot observations

Few bright calibrators

Highly-populated fields
Dataset contains fixed amount of
information – antennas, channels, time
How well can we measure
the parameters of a model
from some data? → The
Cramer-Rao bound
The Fisher Information: the
Information contained within a dataset
- Precision on point
source parameters: noise
level (σ) set by Tsys, Δν, Δt
- Iu, Iv, Iuv dependent on
array configuration
- long baselines yield
more information, but all
baselines important
Pos'n
Pos'n
Flux
Dataset contains fixed amount of
information – antennas, channels, time
How well can we measure
the parameters of a model
from some data? → The
Cramer-Rao bound
Thermal noise
- Precision on point
source parameters: noise
level (σ) set by Tsys, Δν, Δt
- Iu, Iv, Iuv dependent on
array configuration
- long baselines yield
more information, but all
baselines important
Pos'n
Array config
Pos'n
Flux
Source flux
Precision on source location –
8 second integration; measured data only
ν = 150 MHz
Tsys = 440K
Precision on source location –
8 second integration; measured data only
Precision on source location –
8 second integration; measured data only
ν = 150 MHz
Tsys = 440K
Residual signal in visibilities is
independent of source strength
Propagate errors to visibilities
→ independent of
source strength
Example application
Propagate errors to EoR power spectrum
→ how does this residual signal
affect statistical EoR estimation?
EoR power spectrum
Hales et al. (1998)
Sequentially peeled sources (> 1 Jy)
 Performed a fully-covariant error propagation
 Visibilities → Power spectrum
 MWA, PAPER

What is the magnitude of this effect, compared with the
thermal noise?
EoR power spectrum residual signal
Thermal noise
Higher LOS
resolution
Residual signal
Core +
ring
Higher angular
resolution
Uniform
Trott, Wayth & Tingay (2012, submitted)
How do we peel sources?
What information should we use?
Previous analysis assumed sequential and independent
peeling of sources from the data alone...
→ no impact of other sources on information available in
dataset
→ measurement dataset alone used for position estimation
Open questions:
→ What is the balance of using the current dataset
versus previous information for estimating source
position?
→ Should we peel sequentially or simultaneously?
Precision on source location –
8 second integration; measured data only
Optimal balance of prior information and
measured data –
ionosphere ~60” variation
Prior information
Use dominant
Data use
dominant
Example prior information: mean over last N measured positions
Optimal balance of prior information and
measured data –
ionosphere ~10” variation
Peeling sources: simultaneous
versus sequential
Two models for peeling sources:
1. Simultaneously estimate positions of all sources from
measured data → non-uniqueness, correlations between
sources, but Gaussian noise in visibilities
2. Subtract previous solution for all but one source, and fit
each source sequentially → data non-Gaussian,
corrupted by errors
→ Which is a better strategy from an information
perspective?
Future work...
Summary
Information content of data limits our ability to
precisely measure parameters (e.g., source flux,
position)

Imprecise parameter estimation propagates to
additional uncertainty in scientifically-relevant metrics

How we observe, calibrate and estimate impact the
utility of our science metrics
